Cloth - Cloth interactions in Blender
To make the cloth collide with itself in the example you described, enable self collision.


In the Physics context of the Properties Panel it is found in the tab Cloth Collision.



Enable Self Collision and ajust the other values accordingly.

From the Blender Documentation.


  Self-collisions
  
  Real cloth cannot permeate itself, so you normally want the cloth to self-collide.
  
  Enable Self Collisions
  
  
    Click this to tell the cloth object that it should not penetrate
    itself. This adds to simulation compute time, but provides more
    realistic results. A flag, viewed from a distance does not need this
    enabled, but a close-up of a cape or blouse on a character should have
    this enabled.
  
  
  Quality
  
  
    For higher self-collision quality just increase the Quality and more
    self collision layers can be solved. Just keep in mind that you need
    to have at least the same Collision Quality value as the Quality
    value.
  
  
  Distance
  
  
    If you encounter problems, you could also change the Min Distance
    value for the self-collisions. The best value is 0.75; for fast things
    you better take 1.0. The value 0.5 is quite risky (most likely many
    penetrations) but also gives some speedup.